Question
A man 1.69 meters tall is walking towards a building at the rate of 1.5 meters per second. If there is a light on the ground 15 meter from the building, how fast is the man's shadow on the building growing shorter when he is 5 meters from the building.
Answers
Steve
If the man's shadow has length s, then using similar triangles, when the man is x meters from the building,
s/15 = 1.69/(15-x)
s = 25.35/(15-x)
ds/dt = 25.25/(15-x)^2 dx/dt
Now plug in your numbers
s/15 = 1.69/(15-x)
s = 25.35/(15-x)
ds/dt = 25.25/(15-x)^2 dx/dt
Now plug in your numbers